OFFSET
0,2
FORMULA
a(n) = Sum_{k=0..n} A132393(n,k)*3^k*8^(n-k).
a(n) = (-5)^n*sum_{k=0..n} (8/5)^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012
G.f.: 2/G(0), where G(k)= 1 + 1/(1 - 2*x*(8*k+3)/(2*x*(8*k+3) - 1 + 16*x*(k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 30 2013
a(n) +(-8*n+5)*a(n-1)=0. - R. J. Mathar, Sep 04 2016
From Ilya Gutkovskiy, Mar 23 2017: (Start)
E.g.f.: 1/(1 - 8*x)^(3/8).
a(n) ~ sqrt(2*Pi)*8^n*n^n/(exp(n)*n^(1/8)*Gamma(3/8)). (End)
Sum_{n>=0} 1/a(n) = 1 + (e/8^5)^(1/8)*(Gamma(3/8) - Gamma(3/8, 1/8)). - Amiram Eldar, Dec 20 2022
EXAMPLE
a(0)=1, a(1)=3, a(2)=3*11=33, a(3)=3*11*19=627, a(4)=3*11*19*27=16929, ...
MATHEMATICA
Join[{1}, FoldList[Times, 8Range[0, 20]+3]] (* Harvey P. Dale, Aug 11 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Sep 20 2008
EXTENSIONS
a(11) corrected by Ilya Gutkovskiy, Mar 23 2017
STATUS
approved